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L.Richter
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Homework Statement
An originally complete ring made of linear elastic material (Young's modulus, E and Poisson's ratio, v) is cut by a saw. A gap, delta, is generated by a pair of forces, P. Determine this force, P. (Use Saint Venant's principle) Inner radius of ring, a. Outer radius, b.
Homework Equations
forces: integral over the area, A of tsubA dA = f
moments: integral over the area, A of tsubA X = M
A = area
t = traction tsubi = sigmasubij dot nsubj where sigma represents stress
f = force
M = moment
boundary conditions?
The Attempt at a Solution
I am in a solid mechanics/stress analysis course and I'm having a problem applying Saint Venant's principle to this problem. My thoughts are that the forces, P (equal and opposite) that are generated by sawing the ring (which looks like a washer cut through the bottom thickness only) would equal the force, P that is internal in an uncut section of the ring. So I would be able to use an uncut ring to determine the force, P?
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